This is a historical post. In this older post (before The Beginning of Infinity was even published) I actually champion Taleb’s idea that we do use a form of “inductive reasoning” as part of the conjecture process. I wouldn’t use this wording today.
As discussed in my last post, if science can’t be justified by inductive reasoning, how do we justify it?
Popper’s own epistemology (i.e. theory of how we gain knowledge) is based around conjecture and refutation.
All knowledge is gained by starting with conjecture. Interestingly, inductive “reasoning” does seem to play a role in this. As documented in the Taleb’s book, The Black Swan: The Impact of the Highly Improbable we humans seem to be wired for “inductive reasoning.” We see non-existent causes and effects everywhere. Taleb gives these questionable cause/effects a name: narrative fallacies. Taleb spends a lot of time discussing the problems with our built in inductive reasoning. But there is an upside. We easily generate conjectures – mostly bad ones.
Refutation is how we manage that built in “conjecture process” to make it productive. Clearly refutation and testability/falsifiability are related concepts. Popper often uses them interchangeably. But there seems to be a subtle difference between the two. One does not have to have an observationally testable theory to be able to effectively refute it.
One of the most effective ways to refute a theory is, according to Popper, to “test the theory under discussion by finding out whether its logical consequences are all acceptable, or whether it has, perhaps some undesirable consequences.” (Myth of the Framework, p. 60)
Here we have a way to criticize and even possibly effectively refute a theory without any sort of observational testability.
Popper takes this idea even further. Conjecture and Refutation is not merely how science progresses, it is how all things progress. For example, Popper sees direct ties between evolution through natural selection and the growth of scientific knowledge. In fact, growth of scientific knowledge may be thought of as a special case of biological evolution.
From a biological or evolutionary point of view, science, or progress in science, may be regarded as a means used by the human species to adapt itself to the environment: to invade new environmental niches, and even to invent new environmental niches. (Myth of the Framework, p. 2)
Popper is careful to not take this connection any further than is realistic. The similarities between genetic adaption and scientific discovery are profound, but not complete.
On all three levels – genetic adaption, adaptive behavior, and scientific discovery – the mechanism of adaption is fundamentally the same. (Myth of the Framework, p. 3)
Popper’s argument is that all three of these are based on what he calls “instruction” and “selection.” In the case of biological evolution the “instruction” is genes (i.e. DNA) that attempt to copy themselves. The “selection” is Darwin’s natural selection process.  For scientific discoveries the “instruction” is textbooks and course work to transmit scientific knowledge and the “selection” is “revolutionary tentative theories.” (Myth of the Framework, p. 3)
Therefore Popper sees all knowledge – even the “knowledge” contained with DNA – as stemming from the conjecture and refutation process. Even growth of knowledge in the arts follows this process. (Myth of the Framework, p. 9)
Of course we will have to admit that there are difference as well. For one thing, biological evolution is not believed to be goal directed. Whereas scientific knowledge grows through purposeful selection, biological evolution is “blind” in this sense. (Myth of the Framework, p. 5)
All this means, Popper claims, that refutation and criticism is the basis for all gains in knowledge.  According to Popper, we only gain knowledge from our mistakes.  More specifically, Popper argues that knowledge is gained through this process of problem solving. We have a problem, we conjecture a solution, we test if it solves the problem. If it does solve the problem, then we now have new problems to deal with. Repeat. In this way, we make growth in knowledge. It is therefore not observation that starts the growth of knowledge, but rather having a problem to be solved. David Deutsch (a Popperite) argues:
Thus contrary to the inductivist scheme… scientific discovery need not begin with observational evidence. But it does always being with a problem. …a set of ideas that seems inadequate and worth trying to improve. (The Fabric of Reality, p. 62)
But Does This Justify Belief in Science?
But does all this justify knowledge? According to Popper and Deutsch, yes, it does. If we have multiple explanations, the “best” explanation is the one that solves the most problems and the deepest problems and we are therefore, on those grounds, justified in accepting it as the most realistic view of reality currently available. Of course things might – actually will – change in the future as we find new problems, better theories, and therefore better explanations. But until that new explanation comes into existence we are justified in believing in the knowledge gained through the conjecture and refutation process. Induction is not needed, nor desired, in this formula for growth of knowledge.
 Actually, Popper argues that biological evolution probably has other selection processes than merely natural selection. But this is besides my point for the moment.
 …refutation and criticism is the basis for all gains in knowledge… As much as I enjoy and agree with Popper, I should note here that I don’t believe conjecture and refutation alone can explain growth of knowledge. But that will be a subject of a future post.
 …we only gain knowledge from our mistakes… “The growth of knowledge, and especially of scientific knowledge, consists in learning from our mistakes.” (Myth of the Framework, p. 93)
Historical Note: footnote 3 is a refutation by Popper of the idea that we should try to not reach beyond our level of knowledge to avoid making too many mistakes. Often making as many mistakes as quickly as possible is desirable.